Robust optimization of uncertain structures based on normalized violation degree of interval constraint

In order to improve the mechanical properties of a structure with uncertain but bounded parameters, a constrained interval robust optimization model is proposed with the center and halfwidth of its most important mechanical performance index described as objectives and the other performance indices described as constraints. The conventional indirect approaches for solving the interval optimization model will result in different optimal solutions when prescribing different satisfactory degrees of interval constraints and also deviates from the original intention of modeling the optimization problem based on interval theory. To overcome the shortcomings of indirect interval optimization approaches, a novel concept of the normalized violation degree of interval constraint (NVDIC) and the NVDIC-based preferential guidelines are proposed for directly sorting different design vectors. A direct interval robust optimization algorithm is proposed, which integrates Kriging models with inner layer genetic algorithms (GAs) to compute the interval bounds of the mechanical performance indices of various design vectors, and realizes the direct sorting of different design vectors by the outer layer non-dominated sorting genetic algorithm (NSGA) according to the NVDIC-based preferential guidelines. The validity of the proposed direct interval robust optimization algorithm is verified by a numeric example, the superiority of which to the conventional indirect one is discussed in detail. Finally, the robust optimization of a press slider with uncertain material properties demonstrates the feasibility and validity of the proposed method in engineering.

[1]  Wei Chen,et al.  Extended Objective-Oriented Sequential Sampling Method for Robust Design of Complex Systems Against Design Uncertainty , 2012 .

[2]  A. Sofi,et al.  Reliability analysis of structures with interval uncertainties under stationary stochastic excitations , 2016 .

[3]  Z. Kang,et al.  Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model , 2009 .

[4]  Zissimos P. Mourelatos,et al.  A single-loop method for reliability-based design optimisation , 2008 .

[5]  Asoke Kumar Bhunia,et al.  A Comparative Study of Different Order Relations of Intervals , 2012, Reliab. Comput..

[6]  Kyung K. Choi,et al.  Dimension reduction method for reliability-based robust design optimization , 2006 .

[7]  C. Jiang,et al.  Optimization of structures with uncertain constraints based on convex model and satisfaction degree of interval , 2007 .

[8]  Nong Zhang,et al.  Interval multi-objective optimisation of structures using adaptive Kriging approximations , 2013 .

[9]  Xiaoping Du,et al.  Probabilistic mechanism analysis with bounded random dimension variables , 2013 .

[10]  Zhan Kang,et al.  On robust design optimization of truss structures with bounded uncertainties , 2013 .

[11]  C. Jiang,et al.  Structural reliability analysis based on random distributions with interval parameters , 2011 .

[12]  Marco de Angelis,et al.  Advanced line sampling for efficient robust reliability analysis , 2015 .

[13]  Pingfeng Wang,et al.  A Maximum Confidence Enhancement Based Sequential Sampling Scheme for Simulation-Based Design , 2013, DAC 2013.

[14]  Shapour Azarm,et al.  A modified Benders decomposition method for efficient robust optimization under interval uncertainty , 2011 .

[15]  Xiaoping Du.  Reliability‐based design optimization with dependent interval variables , 2012 .

[16]  Sukhamay Kundu,et al.  Min-transitivity of fuzzy leftness relationship and its application to decision making , 1997, Fuzzy Sets Syst..

[17]  S. Chanas,et al.  Multiobjective programming in optimization of interval objective functions -- A generalized approach , 1996 .

[18]  Xu Han,et al.  Uncertain optimization of composite laminated plates using a nonlinear interval number programming method , 2008 .

[19]  Jyh-Cheng Yu,et al.  Design for Robustness Based on Manufacturing Variation Patterns , 1998 .

[20]  I. Doltsinis,et al.  ROBUST DESIGN OF STRUCTURES USING OPTIMIZATION METHODS , 2004 .

[21]  B. Hu,et al.  A Novel Approach in Uncertain Programming Part II: A Class of Constrained Nonlinear Programming Problems with Interval Objective Functions , 2006 .

[22]  Kyung K. Choi,et al.  A new response surface methodology for reliability-based design optimization , 2004 .

[23]  Yixiong Feng,et al.  Interval multiobjective optimization of structures based on radial basis function, interval analysis, and NSGA-II , 2014 .

[24]  Jianmin Zhu,et al.  Performance Distribution Analysis and Robust Design , 2001 .

[25]  Michael Beer,et al.  Designing robust structures - A nonlinear simulation based approach , 2008 .

[26]  Jianrong Tan,et al.  Direct optimization of uncertain structures based on degree of interval constraint violation , 2016 .

[27]  Kyung K. Choi,et al.  Integration of Possibility-Based Optimization and Robust Design for Epistemic Uncertainty , 2007 .

[28]  T. Simpson,et al.  Comparative studies of metamodelling techniques under multiple modelling criteria , 2001 .

[29]  Yakov Ben-Haim,et al.  Discussion on: A non-probabilistic concept of reliability , 1995 .

[30]  Z. Luo,et al.  A new interval uncertain optimization method for structures using Chebyshev surrogate models , 2015 .

[31]  Kyung K. Choi,et al.  Alternative Methods for Reliability-Based Robust Design Optimization Including Dimension Reduction Method , 2006, DAC 2006.

[32]  Ramon E. Moore.  Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[33]  V. I. Levin,et al.  Ordering of Intervals and Optimization Problems with Interval Parameters , 2004 .

[34]  R. Niu.  Invited: Inverse analysis of heat transfer across a multilayer composite wall with Cauchy boundary conditions , 2014 .

[35]  Xiaojun Wang,et al.  Actuator placement robust optimization for vibration control system with interval parameters , 2015 .

[36]  B. Hu,et al.  A novel approach in uncertain programming part I: new arithmetic and order relation for interval numbers , 2006 .

[37]  Xu Han,et al.  A novel evidence-theory-based reliability analysis method for structures with epistemic uncertainty , 2013 .

[38]  H. Ishibuchi,et al.  Multiobjective programming in optimization of the interval objective function , 1990 .

[39]  Jianrong Tan,et al.  Robust optimization of structural dynamic characteristics based on adaptive Kriging model and CNSGA , 2015 .

[40]  Richard J. Balling,et al.  Consideration of Worst-Case Manufacturing Tolerances in Design Optimization , 1986 .

[41]  Kwon-Hee Lee,et al.  Robust optimization considering tolerances of design variables , 2001 .

[42]  Gyung-Jin Park,et al.  Development of a Robust Design Process Using a New Robustness Index , 2005, DAC 2005.

[43]  Karim Abdel-Malek,et al.  Fuzzy tolerance multilevel approach for structural topology optimization , 2006 .

[44]  Jacques Periaux,et al.  Uncertainty based robust optimization method for drag minimization problems in aerodynamics , 2012 .

[45]  Xiaoping Du,et al.  Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design , 2004, DAC 2002.

[46]  Zhiping Qiu,et al.  Improved numerical prediction and reliability-based optimization of transient heat conduction problem with interval parameters , 2015 .

[47]  Liping Chen,et al.  Interval uncertain method for multibody mechanical systems using Chebyshev inclusion functions , 2013 .

[48]  C. Jiang,et al.  A sequential nonlinear interval number programming method for uncertain structures , 2008 .

[49]  Farrokh Mistree,et al.  Integration of the Response Surface Methodology with the Compromise Decision Support Problem in Developing a General Robust Design Procedure , 1994 .